There aren’t that many words that have two different plural forms. Most of these are loanwords, often from Latin or its descendent languages.
For loanwords, the first stage of loanword incorporation into German is to leave it as it is and to form a plural by simply adding an s. (For loanwords that end in -s, things get difficult and different.) Thus, Pizzas was the earlier way to pluralise Pizza in German.
As loanwords get more and more familiar, they are often more formally incorporated into grammar rules. In German, the most typical plural endings of native words are -e, -er and -en and Pizza fits with the -en type so Pizzen later appeared. Note that neither of these is correct in Italian where pizze is the only acceptable plural.
For most of these loanwords with multiple plural forms, it does not matter which form you use. Both zwei Pizzen and zwei Pizzas are perfectly acceptable and there is no difference between the two. By the way: some dictionaries may note the plurals in a different order; that is often a clear argument for them being equivalent.
Sometimes, even native German words have two different plural forms, and that is where you want to be careful. For example, Wort has both the plural Wörter and Worte. These cannot be used interchangeably: Wörter signifies a number of letter clusters separated by spaces while Worte is a collection of what somebody said.
Unter den Worten Jesu sticht besonders die Bergpredigt hervor.
Der vorige Satz hat neun Wörter.
As mentioned, this typically only applies to native words, i.e. non-loanwords.